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Resilient Dynamic Programming

Saverio Caminiti, Irene Finocchi, Emanuele G. Fusco, Francesco Silvestri
2015 Algorithmica  
We investigate the design of dynamic programming algorithms in unreliable memories, i.e., in the presence of errors that lead the logical state of some bits to be read differently from how they were last written. Assuming that a limited number of memory faults can be inserted at run-time by an adversary with unbounded computational power, we obtain the first resilient algorithms for a broad range of dynamic programming problems, devising a general framework that can be applied to both iterative
more » ... and recursive implementations. Besides all local dependency problems, where updates to table entries are determined by the contents of neighboring cells, we also settle challenging non-local problems, such as all-pairs shortest paths and matrix multiplication. All our algorithms are correct with high probability and match the running time of their standard non-resilient counterparts while tolerating a polynomial number of faults. The recursive algorithms are also cacheefficient and can tolerate faults at any level of the memory hierarchy. Our results exploit a careful combination of data replication, majority techniques, fingerprint computations, and lazy fault detection. To cope with the complex data access patterns induced by some of our algorithms, we also devise amplified fingerprints, which might be of independent interest in the design of resilient algorithms for different problems.
doi:10.1007/s00453-015-0073-z fatcat:c6lzvh2ahnd4lfulgxseys6qha

Knowledge, Level of Symmetry, and Time of Leader Election [article]

Emanuele G. Fusco, Andrzej Pelc
2015 arXiv   pre-print
Figure 5 5 : a) Graph G 2 . b) Graph G 2 .  ...  Let G be any graph in class C. If leader election is possible for the graph G, then it is accomplished. • Strong LE. Let G be any graph in class C.  ... 
arXiv:1508.01300v1 fatcat:guoo2yyyjvcjxmn77rbsx5xvri

Topology recognition with advice

Emanuele G. Fusco, Andrzej Pelc, Rossella Petreschi
2016 Information and Computation  
, G 1 or G 2 G 2 , G 1 , or G 2 .  ...  Figure 1 : a) Graphs G 1 and G 2 from [31] . b) Graphs G 1 and G 2 . c) Schematic representation of graphs H 1 and H 2 , in which the rectangle represents one of the graphs G 1 , (b) G 2 (c) G 1 , G 2  ... 
doi:10.1016/j.ic.2016.01.005 fatcat:kh6ret3h3vfpvleix3ojh66l7i

Distributed tree comparison with nodes of limited memory

Emanuele G. Fusco, Andrzej Pelc
2012 Networks  
. , k−1, let |g i (σ)| denote the number of messages in g i (σ).  ...  . , k − 1, there is a subset of at least 2 j+1 instances σ, such that |g i (σ)| ≥ j/x.  ...  . , k − 1 and any distinct instances σ, σ from Σ, we have g i (σ) = g i (σ ).  ... 
doi:10.1002/net.21463 fatcat:3xwuhphpvrfnbm6ohofennixlm

Learning a Ring Cheaply and Fast [chapter]

Emanuele G. Fusco, Andrzej Pelc, Rossella Petreschi
2013 Lecture Notes in Computer Science  
By the definition of communication delay induced on a path, we have g({x h+p , x h+p+1 }, r p ) = 1, for all 0 ≤ p < D. We now show that sets Z y are pairwise disjoint.  ...  Elements of Z y are ordered pairs composed of an edge and a round number, of the form ({x h+p , x h+p+1 }, r p ), for 0 ≤ p < D, where r p = δ( x h . . . x h+p+1 , g) + p + 1.  ... 
doi:10.1007/978-3-642-39212-2_49 fatcat:4qdyntjb3veqdkdx2ea4oph2fe

How much memory is needed for leader election

Emanuele G. Fusco, Andrzej Pelc
2011 Distributed computing  
Let G be any graph in class C. If leader election is possible for the graph G, then LE is accomplished. • Strong LE. Let G be any graph in class C.  ...  If leader election is possible for the graph G, then LE is accomplished.  ... 
doi:10.1007/s00446-011-0131-y fatcat:uraxymdl6rfyvjwgm7bwxiuefa

Acknowledged broadcasting in ad hoc radio networks

Emanuele G. Fusco, Andrzej Pelc
2008 Information Processing Letters  
We consider ad hoc radio networks in which each node knows only its own identity but is unaware of the topology of the network, or of any bound on its size or diameter. Acknowledged broadcasting (AB) is a communication task consisting in transmitting a message from a distinguished source to all other nodes of the network and making this fact common knowledge among all nodes. To do this, the underlying directed graph must be strongly connected. Working in a model allowing all nodes to transmit
more » ... ontaneously even before getting the source message, Chlebus et al. [6] proved that AB is impossible, if collision detection is not available, and gave an AB algorithm using collision detection that works in time O(nD) where n is the number of nodes and D is the eccentricity of the source. Uchida et al. [29] showed an AB algorithm without collision detection working in time O(n 4/3 log 10/3 n) for all strongly connected networks of size at least 2. In particular, it follows that the impossibility result from [6] is really caused by the singleton network for which AB amounts to realize that the source is alone. We improve those two results by presenting two generic AB algorithms using a broadcasting algorithm without acknowledgement, as a procedure. For a large class of broadcasting algorithms the resulting AB algorithm has the same time complexity. Using the currently best known broadcasting algorithms, we obtain an AB algorithm with collision detection working in time O(min{n log 2 D, n log n log log n}), for arbitrary strongly connected networks, and an AB algorithm without collision detection working in time O(n log n log log n) for all strongly connected networks of size n ≥ 2. Moreover, we show that in the model in which only nodes that already got the source message can transmit, AB is infeasible in a strong sense: for any AB algorithm there exists an infinite family of networks for which this algorithm is incorrect.
doi:10.1016/j.ipl.2008.09.011 fatcat:udzaqc7vjje2fphof2i46zgrci

Knowledge, level of symmetry, and time of leader election

Emanuele G. Fusco, Andrzej Pelc
2014 Distributed computing  
Let G be any graph in class C. If leader election is possible for the graph G, then it is accomplished. -Strong leader election. Let G be any graph in class C.  ...  Let G be a graph. The following conditions are equivalent: 1. Leader election is possible in G; 2. Views of all nodes are different; 3. There exists a node with a unique view.  ... 
doi:10.1007/s00446-014-0237-0 fatcat:l653tdifujdx5ob5opus24j5x4

How Much Memory Is Needed for Leader Election [chapter]

Emanuele G. Fusco, Andrzej Pelc
2010 Lecture Notes in Computer Science  
Let G be any graph in class C. If leader election is possible for the graph G, then LE is accomplished. • Strong LE. Let G be any graph in class C.  ...  If leader election is possible for the graph G, then LE is accomplished.  ... 
doi:10.1007/978-3-642-15763-9_25 fatcat:xrhi247zfreuxd4nr4qusm72fy

Broadcasting in UDG radio networks with missing and inaccurate information

Emanuele G. Fusco, Andrzej Pelc
2010 Distributed computing  
They proved that the minimum broadcasting time is Θ'min˘D + g 2 , D log g¯´, assuming that each node knows the density of the network and knows exactly its own position in the plane.  ...  Nevertheless, under our very weak scenario, we construct a broadcasting algorithm that maintains optimal time O'min˘D + g 2 , D log g¯´for all networks with at least 2 nodes, of diameter D and granularity  ...  (g 2 ).  ... 
doi:10.1007/s00446-010-0093-5 fatcat:uazll5wrvrgw7lyfj66dyljjum

Knowledge, Level of Symmetry, and Time of Leader Election [chapter]

Emanuele G. Fusco, Andrzej Pelc
2012 Lecture Notes in Computer Science  
Let G be any graph in class C. If leader election is possible for the graph G, then it is accomplished. -Strong leader election. Let G be any graph in class C.  ...  Let G be a graph. The following conditions are equivalent: 1. Leader election is possible in G; 2. Views of all nodes are different; 3. There exists a node with a unique view.  ... 
doi:10.1007/978-3-642-33090-2_42 fatcat:nxp4kutxp5gx7ngkkh3ov7sltm

Communication Complexity of Consensus in Anonymous Message Passing Systems [chapter]

Emanuele G. Fusco, Andrzej Pelc
2011 Lecture Notes in Computer Science  
Let G be a fully symmetric connected n-node graph. Then there exists a fully symmetric connected spanning subgraph G of G with at most n log n edges.  ...  visit of G starting from u to the node having the same number in the breadth-first visit of G starting from v.  ... 
doi:10.1007/978-3-642-25873-2_14 fatcat:iycm4mrwpba7hcbq4pgsuwvoyy

Trade-offs Between the Size of Advice and Broadcasting Time in Trees

Emanuele G. Fusco, Andrzej Pelc
2009 Algorithmica  
We study the problem of the amount of information required to perform fast broadcasting in tree networks. The source located at the root of a tree has to disseminate a message to all nodes. In each round each informed node can transmit to one child. Nodes do not know the topology of the tree but an oracle knowing it can give a string of bits of advice to the source which can then pass it down the tree with the source message. The quality of a broadcasting algorithm with advice is measured by
more » ... competitive ratio: the worst case ratio, taken over n-node trees, between the time of this algorithm and the optimal broadcasting time in the given tree. Our goal is to find a trade-off between the size of advice and the best competitive ratio of a broadcasting algorithm for n-node trees. We establish such a trade-off with an approximation factor of O(n ), for an arbitrarily small positive constant . This is the first problem for which a trade-off between the amount of provided information and the efficiency of the solution is shown for arbitrary size of advice.
doi:10.1007/s00453-009-9361-9 fatcat:skjwaw4nd5fuxm443ovruhfnfu

L(h,1,1)-Labeling of Outerplanar Graphs [chapter]

Tiziana Calamoneri, Emanuele G. Fusco, Richard B. Tan, Paola Vocca
2006 Lecture Notes in Computer Science  
Any OBFT(G) of an outerplanar graph G is an outerplanar embedding of G. Proof.  ...  Let G be an outerplanar graph with its associated OBFT(G), and two siblings x and y, x < y, in OBFT(G).  ... 
doi:10.1007/11780823_21 fatcat:qyqwubzahnf2hgao5rkvumqn5a

Impact of Information on the Complexity of Asynchronous Radio Broadcasting [chapter]

Tiziana Calamoneri, Emanuele G. Fusco, Andrzej Pelc
2008 Lecture Notes in Computer Science  
(g = 1/d); c, α and β are constants.  ...  In this case, in the formulae for the upper and lower bounds on the work, the parameter g = 1/d should be replaced by g = 1/d .  ... 
doi:10.1007/978-3-540-92221-6_21 fatcat:wbsq54nxhfcjtpm62akmvcp5ti
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